Q3 of 59 Page 82

In figure 3.79, O is the centre of the circle and B is a point of contact. seg OE seg AD, AB = 12, AC = 8, find


(1) AD


(2) DC


(3) DE.


(1)Given: OE AD, AB = 12, AC = 8


⇒ AD × AC = AB2


This property is known as tangent secant segments theorem.


⇒ AD × 8 = 122



(2)DC = AD – AC = 18 – 8 = 10


(3)As we know that a perpendicular from centre divides the chord in two equal parts. Here, OE AD.


⇒ DE = EC


⇒ DE + EC = DC


⇒2DE = DC



More from this chapter

All 59 →
1

In figure 3.77, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.


 2

In figure 3.78, chord MN and chord RS intersect at point D.

(1) If RD = 15, DS = 4, MD = 8 find DN


(2) If RS = 18, MD = 9, DN = 8 find DS



 4

In figure 3.80, if PQ = 6, QR = 10, PS = 8 find TS.


 5

In figure 3.81, seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DE × GE = 4r2